非齐次线性微分方程的有限级解

Finite order solutions of non-homogeneous linear differential equations with entire coefficients

摘要: 研究了非齐次线性微分方程f^(k)+A_k-1(z)f^(k-1)+\cdots+A_1(z)f'+A_0(z)f=F(z) 有限级解的增长性,其中A_j(z)\hspace0.2cm(j=0,\cdots,k-1)和F(z) 都是整函数,并且存在某个A_s(z)在某个扇形内以指数的形式起支配作用.

Abstract: The growth of finite order solutions of non-homogeneous linear differential equation f^(k)+A_k-1(z)f^(k-1)+\cdots+A_1(z)f'+A_0(z)f=F(z) is considered, where A_j(z),~j=0,\cdots,k-1,~F(z) are entire functions,and there exists some A_s(z) as exponentially dominating in a sector.